%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SEU161+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 17:51:18 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU161+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.35  % Computer : n019.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Wed Aug 23 20:04:13 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 0.20/0.61  Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.61  
% 0.20/0.61  % SZS status Theorem
% 0.20/0.61  
% 0.20/0.61  % SZS output start Proof
% 0.20/0.61  Take the following subset of the input axioms:
% 0.20/0.61    fof(l23_zfmisc_1, lemma, ![B, A2]: (in(A2, B) => set_union2(singleton(A2), B)=B)).
% 0.20/0.61    fof(t46_zfmisc_1, conjecture, ![A, B2]: (in(A, B2) => set_union2(singleton(A), B2)=B2)).
% 0.20/0.61  
% 0.20/0.61  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.61  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.61  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.61    fresh(y, y, x1...xn) = u
% 0.20/0.61    C => fresh(s, t, x1...xn) = v
% 0.20/0.61  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.61  variables of u and v.
% 0.20/0.61  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.61  input problem has no model of domain size 1).
% 0.20/0.61  
% 0.20/0.61  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.61  
% 0.20/0.61  Axiom 1 (t46_zfmisc_1): in(a, b) = true2.
% 0.20/0.61  Axiom 2 (l23_zfmisc_1): fresh14(X, X, Y, Z) = Z.
% 0.20/0.61  Axiom 3 (l23_zfmisc_1): fresh14(in(X, Y), true2, X, Y) = set_union2(singleton(X), Y).
% 0.20/0.61  
% 0.20/0.61  Goal 1 (t46_zfmisc_1_1): set_union2(singleton(a), b) = b.
% 0.20/0.61  Proof:
% 0.20/0.61    set_union2(singleton(a), b)
% 0.20/0.61  = { by axiom 3 (l23_zfmisc_1) R->L }
% 0.20/0.61    fresh14(in(a, b), true2, a, b)
% 0.20/0.61  = { by axiom 1 (t46_zfmisc_1) }
% 0.20/0.61    fresh14(true2, true2, a, b)
% 0.20/0.61  = { by axiom 2 (l23_zfmisc_1) }
% 0.20/0.61    b
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  
% 0.20/0.61  RESULT: Theorem (the conjecture is true).
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